Name: _____________________________________
Period: _________
th
Date: ___________________
th
7 Pre-AP REVIEW for Test1 4 Six Weeks
Know Angle Relationships:
• Complementary: add up to 90o
• Supplementary: add up to 180o
• Vertical: opposite angles are congruent
• 180o in triangles
• 360o in quadrilaterals
Know geometric figures by their description and be
able to classify them.
• Isosceles Triangle: 2 equal sides, 2 equal angles
• Equilateral Triangle: three 60o angles, 3 equal sides
• Trapezoid: 2 parallel sides, 2 non-parallel sides
• Rhombus: 4 equal sides
• Square: 4 equal sides, 4 right angles
• Parallelogram: opposite sides are parallel,
opposite sides are equal, opposite angles are equal;
any 2 consecutive angles are supplementary
• Regular polygons: All sides are equal and all angles
are equal
Area and Perimeter:
• Triangles, Squares, Rectangles, Trapezoids,
Composite Figures
• Identify area formulas that will solve problems
including those that require working backward.
Example: If you are given the area, which formula
below would let you find the height of the triangle?
Similar Figures:
• Be able to identify the corresponding parts
• Be able to use ratio tables or cross products to find
missing information (indirect measurement)
• Know how to solve shadow problems, overlapping
triangles, “bow-tie” triangles.
• Be able to identify proportions that will solve
indirect measurement problems.
1. Consider the following diagram.
What is the value of x?
A 14 o
B 28 o
C 62o
D 76 o
2. The triangle in the picture below represents part of a
house.
Based on the angle measure in the picture, what is
the value of x? Classify the triangle by 2 names.
Value of x: ___________________
Classify triangle: ____________, ____________
3. Which angle is the complement to KQM in the
following diagram?
4. Study the figure below.
In the figure, line RT is straight. What is the measure
of angle RSQ?
___________________
5. In the figure below, the three lines intersect at a
point. If x = 120o and z = 40o, what is the value of y?
11. A triangle could have which of the following sets of
angles?
A. 90⁰, 70⁰, 10⁰
B. 65⁰, 75⁰, 50⁰
C. 110⁰, 35⁰, 35⁰
x⁰
D. 15⁰, 90⁰, 95⁰
z⁰
y⁰
________________
6. Find the measure of the complement of an angle with
measure 47o.
________________
7. Find the measure of the supplement of an angle with
measure 128o.
________________
8. Classify triangle ABC by 2 names.
12. Which of the following describes a triangle that has
sides of 3 centimeters, 3 centimeters, and 4
centimeters, and angles that measure 70 degrees, 70
degrees, and 40 degrees?
A.
B.
C.
D.
An acute isosceles triangle
An obtuse scalene triangle
A right isosceles triangle
An acute equilateral triangle
13. In triangle LMN, ∠𝐿𝑀𝑁 = 45°, and ∠𝑀𝑁𝐿 = 90°.
What is the measure of ∠𝐿?
14. What is the measure of ∠x in the quadrilateral
below?
B
5
A
________________
5
5
C
________________
________________
Is this a regular polygon or non-regular polygon?
9. Triangle XYZ has two angles that measure 35⁰ .
Classify triangle XYZ by two names.
________________
________________
10. A right triangle has an angle that is 35⁰. What are
the measures of the other two angles?
________________
________________
15. The lengths of the two legs of an isosceles triangle
are represented by the expressions (2x - 5) and
(x + 7). The perimeter of the triangle is 50 cm. Find
the length of the base of the triangle.
A 11 cm
B 19 cm
C 12 cm
D 26 cm
E 32 cm
16. The lengths of two sides of a triangle are 5 inches
and 8 inches. If the triangle is an isosceles triangle,
which could be the length of the third side?
A.
B.
C.
D.
7 in.
6 in.
5 in.
4 in.
20. A building that has a rectangular base is surrounded
by a sidewalk. The width of the sidewalk, s, is the
same on all four sides of the building. Some of the
dimensions of the building and sidewalk are shown
in the diagram below.
17. Which congruence statement represents the
triangles below?
The total area of the base of the building and
sidewalk is 4256 square feet.
Which of the following equations could be used to
find s, the width in feet of the sidewalk?
18. The diagram below shows a trapezoid and its
dimensions.
What is the area of the
trapezoid?
A. 156 sq. ft.
B. 195 sq. ft.
C. 312 sq. ft.
D. 405 sq. ft.
19. The length of a rectangle is 5 meters more than its
width. The perimeter is 66 meters. Find the area of
the rectangle.
21. Dan is making a rectangular flower box. He is using
wood that is 2 inches wide to make the flower box.
The diagram below shows how the completed
flower box will look from above.
What is the perimeter, in inches, of the outside of
the flower box?
22. Equilateral triangle BCE rests on top of square
ABCD. The area of the square is 64. What is the
perimeter of the triangle?
25. The Texas state flag is rectangular and has a widthto-length ratio of 2:3. Which of the following can
be used to find l, the length of a Texas state flag
with a width of 28 inches?
23. The area of a triangle is 16 square feet, and its
height is 4 feet. What is the length of the base?
You MUST be able to solve this by working
backwards THROUGH THE FORMULA!!!!
Formula: __________________________________
26. ∆ABC is similar to ∆EFG. Find the value of x.
Substitution: ______________________________
Solve:
24. Pentagon ABCDE is similar to pentagon NPQLM, as
shown below.
What is the value of ∠N + ∠L?
27. Two similar quadrilaterals are shown below. The
ratio of the lengths of the corresponding sides �����
𝑀𝑁
���� is 2:3, respectively.
and 𝑆𝑇
���� ?
What is the measure of 𝑅𝑆
A 18 centimeters
B 15 centimeters
C 14 centimeters
D 8 centimeters
28. Triangles QRS and TUV are similar. What is the
����?
length of QR
30. Rectangles GHIJ and KLMN are similar. What is the
����?
length of 𝐿𝑀
A 1.5 cm
B 5 cm
C 6.5 cm
D 7.5 cm
A 1.5 inches
B 3 inches
C 4 inches
D 6 inches
31. Jake wanted to measure the length, l, of the pond,
so he drew this diagram of two similar triangles.
29. Rectangle GHIJ ~ rectangle KLMN, as shown in
the diagram below.
What is the length of the pond? Round to the
nearest foot.
The area of rectangle KLMN is 12 square
centimeters. Based on the dimensions in the
diagram, what is the length of ���
𝐽𝐼
A. 9 cm
B. 10 cm
C. 15 cm
D. 24 cm
(SKIP. Scale Factor problem)
32. Austin has a project due for history. He wants to
enlarge a picture that is 3 inches tall and 5 inches
wide into a similar picture that has a similarity ratio
of 2:5. What will be the dimensions of the new
photo?
33. Find the height of the telephone pole.
34. Sam built a ramp to a loading dock. The ramp has a
vertical support 2 m from the base of the loading
dock and 3 m from the base of the ramp. If the
vertical support is 1.2 m in height, what is the
height of the loading dock?
36. Quadrilateral WXYZ is similar to quadrilateral
LMNP. Find the values of x and y.
37. You are making a large gingerbread house that is
similar in shape to a real house. The real house is
25 feet tall and 40 feet wide. The gingerbread
house is 2.5 feet tall. How wide should you make
the gingerbread house?
38. Parallelogram ABCD is shown below. m∠A
is 5 times m∠B. What is m∠C?
________________
35.
39. Doris drew two similar rectangles. The length of
the larger rectangle is 32 centimeters, and the
width of the larger rectangle is 11 centimeters. The
length of the smaller rectangle is 10 centimeters.
Let w = the width of the smaller rectangle.
Which proportion could Doris use to determine the
width of the smaller rectangle?
A.
32
B.
11
C.
D.
11
32
𝑤
32
𝑤
11
=
=
=
=
10
𝑤
10
𝑤
10
11
32
10